The spectrum of large powers of the Laplacian in bounded domains

Abstract

We present exact results for the spectrum of the Nth power of the Laplacian in a bounded domain. We begin with the one dimensional case and show that the whole spectrum can be obtained in the limit of large N. We also show that it is a useful numerical approach valid for any N. Finally, we discuss implications of this work and present its possible extensions for non integer N and for 3D Laplacian problems.

13 pages, 2 figures

References in corpus (2)

• Fractional Laplacian in Bounded Domains
• Average Time Spent by Levy Flights and Walks on an Interval with Absorbing Boundaries

Cited by in corpus (3)

• The Spectrum of the Fractional Laplacian and First Passage Time Statistics
• Seeing asymptotic freedom in an exact correlator of a large-$N$ matrix field theory
• The universal coefficient of the exact correlator of a large-$N$ matrix field theory